#### LARS Tech Report Number

111872

#### Abstract

The machine processing of spatially variant multitemporal data such as imagery obtained at different times requires that these data be in geometrical registration such that the analysis processor may obtain the datum for a specified ground resolution element in each of the sets of imagery being utilized for analysis.

Misregistration between corresponding subsets of imagery contains both a displacement and a geometrical distortion component, and the affine transformation is postulated to characterize this misregistration between data subsets. Search techniques utilizing the moduli of the Fourier Transforms of these data are developed for estimating the coefficients of geometrical distortion components of this model.

Following the correction of these distortion components, the displacement is located by the crosscorrelation of a template obtained from one set of data, termed the reference, with the second, or background data. This template, derived for the optimum discrimination of the reference data embedded in the background, is determined by the solution of a system of equations involving the reference data and the covariance matrix of these data.

The derivation of the optimum filter includes constraints such that the maximum filter output, corresponding to the correct superposition of the reference template on the background data, is unity and the energy in the filter is finite. The filter obtained in this development is linear although it may involve a parameter requiring the solution of a nonlinear equation.

The performance of the crosscorrelation algorithm is evaluated using ideal data obtained by convolving an array of computer generated random numbers with a two-dimensional lowpass filter having a specified impulse response. The results obtained from these data generally substantiate the conclusions drawn from the analysis of this algorithm. The correlator output is then obtained for noise free and distortionless line scanner data. In these data the reference is selected as a subimage of the background data, and the data are selected to typify line scanner imagery. Multitemporal data are processed with the algorithms developed for the noise-free data to evaluate the applicability of this filter to the conjugate point problem.

It is demonstrated that the crosscorrelation of the template derived from the reference data will not yield useful results unless the geometrical correction of the data is implemented. The Fourier transform search techniques are used to estimate the distortion model coefficients, and a bilinear interpolation algorithm is utilized to correct the imagery. Results of the processor output using the corrected data are given. It is shown that the optimum filter yields a more discriminable peak of the correlation surface at the correct superposition of the reference template on the background than does the filter chosen as a subimage of the reference data itself.

#### Date of this Version

January 1972